A source of sound attached to the bob of a simple pendulum execute `SHM` . The difference between the apparent frequency of sound as received by an observer during its approach and recession at the mean frequency of the source . The velocity of the source at the mean position is ( velocity of sound in the air is `340 m//s`)
[Assume velocity of sound `lt lt` velocity of sound in air ]

Options

A. `1.4 m//s`
B. `3.4 m//s`
C. `1.7 m//s`
D. `2.1 m//s`

Answer

B

Explanation

` f_(1) = f_(0) ((V_(0))/(V_(0) - V)) f_(2) = f_(0)((V_(0))/(V_(0) + V))`
`f_(1) - f_(2) = f_(0) V_(0) ((1)/( V_(0) - V) - (1)/( V_(0) + V))`
` = f_(0) V_(0) (V_(0) + V - V_(0) + V)/( V_(0)^(2) - V^(2)) = f_(0) V_(0) xx ( 2V)/( V_(0)^(2)) = f_(0) ( 2V)/( V_(0))`
given `( 2 Vf_(0))/(V_(0)) = 0.02 xx f_(0) rArr V = 0.01 V_(0) = 3.4 m//s`.